Division Dinoflagellata Engl. (1903) see Superclass Dinoflagellata Bütschli, 1885
   Subdivision Dinokaryota Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Superclass Dinokaryota Fensome et al., 1993
     Class Dinophyceae Pascher (1914)
       Subclass Peridiniphycidae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993)
         Order Peridiniales Haeckel (1894)
           Suborder Peridiniineae Poche (1913) see Order Peridiniales Haeckel (1894)
             Family Peridiniaceae Ehrenb. (1831)
               Subfamily Calciodinelloideae Fensome, F.J.R. Taylor, G. Norris, Sarjeant, Wharton & G.L. Williams (1993) see Family Calciodinellaceae Deflandre (1947)
                 01 Genus †Alasphaera Keupp (1979)
                 02 Genus †Bicarinellum Deflandre (1948)
                 03 Genus †Calcicarpinum Deflandre (1948)
                 04 Genus †Calcigonellum Deflandre (1949)
                 05 Genus †Calciodinellum Deflandre (1947)
                 06 Genus †Calcipterellum Deflandre (1948)
                 07 Genus †Carinellum Keupp (1981)
                 08 Genus †Cubodinellum Keupp (1987)
                 09 Genus †Dimorphosphaera Keupp (1979)
                 10 Genus †Echinodinella Keupp (1980)
                 11 Genus Ensiculifera Balech (1967)
                 12 Genus †Gonellum Keupp (1987)
                 13 Genus †Heptasphaera Keupp (1979)
                 14 Genus †Keuppisphaera Lentin & G.L. Williams (1989)
                 15 Genus †Nephrodinella Keupp (1981)
                 16 Genus †Orthocarinellum Keupp (1987)
                 17 Genus †Orthopithonella Keupp (1984)
                 18 Genus †Pirumella H.M. Bolli (1980)
                 19 Genus Pithonella T. Lorenz (1902)
                 20 Genus †Praecalcigonellum Keupp & Versteegh (1989)
                 21 Genus Scrippsiella Balech ex A.R. Loebl. (1965)
                 22 Genus †Sliteria Krasheninnikov & Basov (1983)
                 23 Genus †Sphaerodinella Keupp & Versteegh (1989) see Genus Calciodinellum Deflandre (1947)
                 24 Genus †Tetramerosphaera H. Willems (1985)
                 25 Genus †Tetratropis H. Willems (1990)